Hey IPizzaJoxenI,
The issue may be as you said and is caused by the amount of devices connected at once. Typically, they should experience a slow down as oppose to a total shut down. If their router is provided by their ISP they can try contacting the ISP and request a new one, or possibly buy a new one. Think of bandwidth as a juice box and each device is like a straw, to some extent no one will be getting enough juice. They can look into improving their internet connection or they can try the following methods to help optimize their connection. Setting up a static ip address will help to create some stability on their connection as well as prevent them from having to reconfigure their ports set up in the future. When setting up your ports, use a DMZ for two of the three consoles, then for the third you can try port forwarding it with the following numbers:
Xbox Ports:
53, 80, 3074 TCP
53, 88, 500, 3074, 3544, 4500 UDP
Call of Duty Ghosts Console Ports:
80, 81,443, 3074, 5223 TCP
36081, 3074, 3075, 3478 UDP.
Let me know if that helps!
Thanks,
^AJ